IngenIeriacutea InvestIgacIoacuten y tecnologiacutea

volumen XIX (nuacutemero 3) julio-septiembre 2018 245 -254ISSN 2594-0732 FI-UNAM artiacuteculo arbitradoRecibido 13 de enero de 2016 Reevaluado 24 de agosto de 2017 Aceptado 23 de octubre de 2017Attribution-NonCommercial-NoDerivatives 40 International (CC BY-NC-ND 40) licenseDOI httpdxdoiorg1022201fi25940732e201819n3021

AbstrAct

The design and simulation of a Full-Bridge Flying-Capacitor Multilevel-Inverter (FB-FCMI) for high-voltage applications are presented The power inverter topology consists of two legs each one with three commutation cells six switches and two flying-capacitors The proposed control system provides twelve square signals for all switches that compose the inverter which is driven at a commutation frequency fSWasymp666 kHz The output frequency f0 is equal to three times the commutation frequency The inductor and capacitor in the resonant-circuit design is calculated based on f0 which depends on the number of cells N The goal of the proposed inverter design is to demonstrate that the output frequency increases as rate of f0 = N∙ fSW In order to show the effect of the increase in the number of cells a resonant power inverter is designed and simulated first with three and then with six switching cells at f0 = 20 kHz Finally the FB-FCMI is connected to the primary winding of the high-voltage transformer while the secondary is coupled to a Dielectric Barrier Discharge reactor represented by its electrical model to generate an electrical discharge in heliumKeywords Multilevel-inverter full-bridge resonant-circuit dielectric barrier discharge electrical model

resumen

Se presenta el disentildeo y simulacioacuten de un Inversor Multinivel de Capacitores Flotados (FB-FCMI por sus siglas en ingleacutes) en puente completo para aplicaciones de alto voltaje La topologiacutea del inversor de potencia consiste en dos ramas cada una con tres ceacutelulas de conmutacioacuten seis interruptores y dos condensadores flotados El sistema de control proporciona doce sentildeales cuadradas para todos los interruptores que componen el inversor que se opera a frecuencia de conmutacioacuten fSWasymp666 kHz La frecuencia de salida es f0 y es igual a tres veces la frecuencia de conmutacioacuten El disentildeo del inductor y condensador del circuito resonante se calcula con base en f0 que estaacute en funcioacuten del nuacutemero de ceacutelulas N El objetivo del disentildeo del inversor propuesto es demostrar que la frecuencia de salida incrementa en proporcioacuten de f0 = N∙ fSW A fin de que se observe el efecto por el incremento en el nuacutemero de ceacutelulas un in-versor resonante de potencia se disentildea y simula primero con tres y despueacutes con seis ceacutelulas de conmutacioacuten a f0 = 20 kHz Final-mente el FB-FCMI se conecta al primario de un transformador de alto voltaje mientras que el secundario se acopla a una descarga de barrera dieleacutectrica para generar una descarga eleacutectrica en helioDescriptores Inversor multicelular puente-completo circuito resonante descarga de barrera dieleacutectrica modelo eleacutectrico

Design and simulation of a resonant full-bridge multicell power inverter for high-voltage applicationsDisentildeo y simulacioacuten de un inversor multicelular de potencia resonante en puente-completo para aplicaciones de alto voltaje

Flores-Fuentes Allan AntonioUniversidad Autoacutenoma del Estado de Meacutexico UAEMexE-mail aafloresfuaemexmx

Peacuterez-Martiacutenez Joseacute ArturoUniversidad Autoacutenoma del Estado de Meacutexico UAEMex E-mail japerezmuamexmx

Garciacutea-Mejiacutea Juan FernandoUniversidad Autoacutenoma del Estado de Meacutexico UAEMexE-mail fgarciamuaemexmx

Rossano-Diacuteaz Ivaacuten OsvaldoUniversidad Autoacutenoma del Estado de Meacutexico UAEMexE-mail iorossanoduaemexmx

Torres-Reyes Carlos EduardoUniversidad Autoacutenoma del Estado de Meacutexico UAEMexE-mail cetorresruaemexmx

Design anD simulation of a resonant full-briDge multicell power inverter for high-voltage applications

IngenIeriacutea InvestIgacIoacuten y tecnologiacutea volumen XIX (nuacutemero 3) julio-septiembre 2018 245-254 ISSN 2594-0732 FI-UNAM246

DOI httpdxdoiorg1022201fi25940732e201819n3021

IntroductIon

After its emergence in the the 90th by Meynard and Foch applications of the Flying Capacitor Multicell In-verters (FCMI) has been continuously growing leading to a wide study in the different areas of the knowledge (Meynard et al 2002) A considerable amount of litera-ture has been published concerning about this kind of static power converter topology on industrial applica-tions for instance STATCOMtrade transport trains active filters to eliminate total harmonic distortion THD cd to cd and cd to ca power converters and more recently in Eolic conversion energy (Rodriguez et al 2012 Abu et al 2010 Fernao et al 2012)Precedent studies about a Three Cell Flying Capacitor Inverter in half-bridge coupled in an electrical model of a Dielectric Barrier Discharge (DBD) are presented by (Flores et al 2009) A simulation of the electrical mo-del is used in order to estimate the experimental results at different gas discharges and operation frequency about 125 and 47 kHz implementing different commu-tation strategies Nevertheless these simulations re-sults are limited to half-bridge and three cells Previous works of the FCMI show a full-bridge configuration applied as electrical source in DBD applications opera-ting at 10-20 kHz (Loacutepez et al 2015) and 125-50 kHz (Peacutentildea et al 2017) In these works experimental and si-mulation results show an agreement application imple-menting this kind of multicell inverter topology operating at high frequency

From the perspective of FCMI technology design switching coupling command signal generator system and high frequency semiconductor drivers are the con-siderable disadvantages not only because specialized components are required but also power losses and technological limitations In fact this kind of power in-verter is usually implemented at low frequency (Zhe et al 2009 Rodriguez et al 2012 Tolbert et al 2000 Sa-mir et al 2010)

Multicell Converters were developed in order to sa-tisfy the electrical characteristics of high voltage and current by Voltage Source Inverter or Current Source Inverter respectively and more recently the high fre-quency operation in the order of hundreds and thou-sands of Hertz In addition the operation frequency in the FCMI is given by f0 = N∙ fSW where fSW is the commu-tation frequency the same that semiconductor devices operation and N is the number of cells configured like one leg in the FCMI structure That property bring-forward an intrinsic characteristic not commonly used in the typical static converters so f0 is proportionally N times than fSW and that statement is an advantage ta-

king in account that semiconductor devices like Thyris-tors GTOs and power BJTs operates at low frequency in the order of some kilo-Hertz at tens to hundreds volts-amperes In counterpart MOSFET and IGBT de-vices operates about tens to hundreds of kilo-Hertz at some tens volts-amperes (Hirofumi 2009) That charac-teristics voltage-current and frequency is a restriction to choose the semiconductor device because the more voltage and current is needed the frequency interval of work is reduced and vice versa (Loren 2003) In the other hand that statement is solved by using the FCMI First its main property consists in distribute the total voltage (VSI) or current (CSI) in the total number of cells N and when the FCMI operates at Fundamental Frequency (F-F) strategy the output operation frequen-cy f0 is given by f0 = N∙ fSW where fSW is the switching frequency equal to the F-F So both characteristics are used in order to overcome the above-mentioned disad-vantages

Moreover until few decades ago the main disadvan-tage of the FCMI is their complexity they require a great number of power devices and a rather complex com-mand firing-circuit made by analog-digital circuits However the current technology based on micro-contro-llers Digital Signal Processor (DSP) Field Program Gate Array (FPGA) and other technologies like Arduinoreg or Raspberrytrade has allowed the higher processing capacity in the control design with any technique implemented such as Simple Square Wave (SSW) or Fundamental Fre-quency (F-F) and Pulse Wide Modulation (PWM) com-monly implemented in the strategy control for FCMI (Holmes and Lipo 2003 Rodriguez et al 2002) The ad-vantage to implement PWM topologies is the reducing of the Total Harmonic Distortion (THD) but as conse-quence large protection circuits (dvdt or didt) are requi-red in order to help the commutation semiconductors and so the losses increase (Aguilloacuten et al 2004)

Considering the above mentioned characteristics about control implementation the proposed FB-FCMI implements an F-F strategy and as a result of the com-mand firing-signals it produces a typical square wave-form output u0 at frequency f0 = N∙ fSW moreover due to fSW is N times lesser than f0 hence the commutation los-ses decrease Actually that property is not commonly applied on this kind of static converters but neverthe-less on this work this feature is improved not only in order to reduce the switching frequency and complexi-ty of the command signals implementation but also the goal of the RLC circuit series with the FB-FCMI achie-ves a resonant operation

As a contribution to operate the FB-FCMI in reso-nant mode converter the design and simulation results

247

Flores-Fuentes AllAn Antonio Peacuterez-MArtiacutenez Joseacute Arturo GArciacuteA-MeJiacuteA JuAn FernAndo rossAno-diacuteAz ivaacuten osvAldo torres-reyes cArlos eduArdo

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are shown The calculus of either L0 and C0 resonant elements is presented Finally the high voltage appli-cation is presented by implementing an electrical mo-del of one dielectric barrier discharge (DBD) The simulation results show the implementation of the FB-FCMI operating at 20 kHz in resonant mode in order to drive a dielectric barrier discharge in helium

sImulAtIon desIgn

Full-bridge Flying CapaCitor MultiCell inverter topology

A resonant FB-FCMI coupled to DBD electrical model is shown in Figure 1 The inverter is constituted by six commutation cells (three upper-leg and three lower-leg) each cell is composed by two complementary MOSFET [M1 M1rsquo] [M2 M2rsquo] [M3 M3rsquo] [M4 M4rsquo] [M5 M5rsquo] and [M6 M6rsquo] every one with its antiparallel diode there is a flying capacitor Cp where p is the posi-tion of cell in upper-leg and Cprsquo in lower-leg

The flying capacitor voltages VC1=VC1rsquo and VC2=VC2rsquo are defined by VCp Cpacute =(rN) sdot VDC where p is the position of the cell in the structure and N is the number of total cells Also the blocking voltage in the MOSFETs is esti-mated by VMN MNacute =(VDCN) and the average current is Ikavg=Ton T∙IS where Ton is the turn-on period T is the total period and IS is the supply current (Meynard et al 2002)

The operation of FB-FCMI is achieving an equal dis-tribution of the total voltage in the blocking-state MOS-

FET This occurs when flying-capacitors are charged at and considering as ideal voltage source The accurate MOSFET firing com-mutation pulses involves that C1=C1rsquo and C2=C2rsquo and that condition guarantees the appropriate voltage and as result the output voltage u0(t) operating at output frequency or Figure 2 shows tree representative commutation pulses [S1 S2 S3] provided to MOSFET M1 M2 and M3 signals are in phase shift 120deg and 240deg respectively the main voltages are pre-sented like output υ0 (t) referenced to upper-leg υW (t) and lower-leg υV (t) So because of the voltage differen-ce between υW (t) and υV (t) is made by υ0 (t)

the resonant rlC series Coupled to Fb-FCMi

As Figure 1 shows a Dielectric Barrier Discharge elec-trical model is coupled to FB-FCMI Then the equiva-lent circuit can be considering by a resonant RLC series circuit Figure 3 shows a resonant RLC series circuit determinate by the inductance LC primary winding of high voltage transformer and the secondary winding capacitance presented in the primary one as CC The analysis of LC-CC values is presented in order to get the resonant operation of the FB-FCMI

The RLC series circuit of the Figure 3 is supplied by the voltage υ0(t) Then the total impedance ZT obtained in frequency domain is given by

CjLjRZT ω

ω 1++= (1)

1 1acute 3C C DCV V= 2 2acute 2 3C C DCV V=

0 3 swf f= sdot 0 3swT T=

Figure 1 Scheme of a three cell resonant FB-FCMI coupled to DBD electrical model

Design anD simulation of a resonant full-briDge multicell power inverter for high-voltage applications

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DOI httpdxdoiorg1022201fi25940732e201819n3021

where ω = 2πf is the angular frequency and f is the linear frequency output f0 The total impedance for the nth fre-quency component

(2)

Then the magnitude and angle impedance values for the nth harmonic are defined as

(3)

(4)

Also the voltage u0(t) is a square signal provided by the FB-FCMI at the resonant RLC series circuit in Fourier term

(5)

where Vm=VDC3 is the maximum amplitude to the out-put square voltage considering only the n odd values So using Ohm law to obtain the output current i0(t) ba-sed on (2) and (5) then

(6)

In an ideal resonant RLC series circuit the i0(t) flow from R to L without losses but the capacitor voltage is in pha-se shifting -π2 radian therefore the capacitor voltage uC(t) is

(7)

Then the total voltage gain Au=uC(t)u0(t) and angle considering the nth harmonic is

(8)

( )2 21( ) 1TZ jn n CR j n LCn C

ω ω ωω

= + -

( ) ( )22 2 21( ) 1TZ jn n CR n LCn C

ω ω ωω

= + -

2 2 1arctan n LCn CRωθ

ω -

=

0 14 1( ) sin( )n

Vmu t nn

ωπ

infin=

=

sum

0 1 2 2 2 2

4 sin( )(t)( ) ( 1)

nVm wC nwti

nwCR n w LCθ

πinfin

=

- = + - sum

1 2 2 2

4 sin( 2)( )( ) ( 1)

C nVm nu tn n CR n LC

ω θ ππ ω ω

infin=

- - = + - sum

2 2

1( )(1 )uA t

jwnCR n w LC=

+ -

S1

S2

S3

Volta

ge

[V]

ʋV(t)

ʋW(t)

ʋ0(t)

3VDC2

VDC2

-VDC2

-3VDC2

VDC2

-VDC2

Tsw

Volta

ge

[V]

Volta

ge

[V]

Tsw3

Tsw3

Time [sec]Figure 3 A resonant RLC series circuit

gm

DS

Mosfet

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Mosfet1

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Mosfet3

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+

Series RLC

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Continuous

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perator

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+

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easurement

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enerator2

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perator

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perator2

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Branch3

i+

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easurement

v+-

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ent1

Scope2Scope3

v+-

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ent2

v+-

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ent3

v+-

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ent4

gm

DS M

osfet3

R

L

C

ʋ0 (t)

ʋR (t)

ʋL (t)

ʋC (t)

i0 (t)

Figure 2 FB-FCMI output voltage υ0(t) upper-leg υV(t) and lower leg υW(t) as a result of accurate commutation strategy [S1 S2 S3]

249

Flores-Fuentes AllAn Antonio Peacuterez-MArtiacutenez Joseacute Arturo GArciacuteA-MeJiacuteA JuAn FernAndo rossAno-diacuteAz ivaacuten osvAldo torres-reyes cArlos eduArdo

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Finally the transfer function magnitude and angle θ in term of quality factor Q at resonant angular fre-quency ω0 are

(9)

(10)

where ω02 = 1LC y Q = 1ωCR

By means (9) and (10) is possible to know the magnitu-de and angle θ as function of parameters Q and factor ff0 so the RLC series circuit is resonance mode when both frequencies either ωω0 or ff0 are the same Hence two work conditions fulfill as

a) Maximum gain voltage υ0(t) υC(t) and b) The output current i0(t) and voltage υ0(t) are in same

phase when Q is maximum as Figure 4a and 4b shown respectively

Figure 5 shows the simulation results of the FB-FC-MI obtained with SIMULINKMATLABreg the voltage υR(t)and current i0(t) values are in the same angle phase ϕ=0 at ff0 condition Otherwise Figure 6 shows the voltages in υR(t) υC(t) and υ0(t) at resonant condition the waveforms evidence the statement f0=3fsw because the output frequency in R or C passive electrical com-ponents is f0asymp20 kHz three times more than commuta-tion frequency fswasymp666 kHz in the voltage υ0(t)

The increasing of the output frequency 0f is a natu-

ral property and benefit of the FB-FCMI when it opera-tes at Fundamental Frequency so not only is an advantage in order to increases the frequency N times but also overcomes the disadvantage of commutation losses at frequency

swf Thus the MOSFET devices operate at

swf the commutation losses are reduced and as consequence snubber circuit protection versus volta-ge dvdt and current didt are diminished

Figure 7a shows the voltage VMN(t) and current IMN(t) through the MOSFET at Zero-Current Switching The ZCS is when the current through a switch is reduced to significantly zero amperes prior to when the switch is being turned either on or off It is due to RLC resonant circuit operation Therefore the advantage is the consi-

uA

22 2

0

1

1 1uA

Qω

ω

=

+ -

-= 1arctan 2

0

2

ωωθ Q

uA

Figure 4 a) Voltage gain magnitude and b) Angle θ as function of quality factor Q and ff0uA

29600 29625 29650 29675 29700

-40

-20

0

20

40

φ=0

u R(t) [V

]

Time [ms]

u0(t) i0(t)

-60

-40

-20

0

20

40

60

i 0(t) [A

]

Figure 5 Voltage υ0(t) and current i0(t) at the same phase φ=0 as a result of resonant condition

a) b)

Design anD simulation of a resonant full-briDge multicell power inverter for high-voltage applications

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derably reduction of power dissipation in the MOS-FETs Figure 7b shows the simulation results on instantaneous power Pi(t) and PRMS in semiconductors the RMS value is ~7 mW

the Fb-FCMi at resonant Mode siMulation set-up

The FB-FMCI showed in Figure 1 is developed and run-ning on SIMULINKMATLABreg using the SimPowerSys-tem libraries In order to get the best performance a previous calculus of RLC resonant components either SimPowerSystem or Funtional-Block was made to achieve the best tuning of the resonant condition The parameter simulation values are f= 20 kHz C=10 nF L=6333 mH R = 1Ω and VM=66 V The simulation parameters on [C1 C1rsquo] and [C2 C2rsquo] are VDC=200 V VC1=VC1rsquo= 13333 V and VC2=VC2rsquo=6666 V also the voltage response of flying ca-pacitors are shown in Figure 8a from this it is possible to sustain the correct values in open-loop control Hence the static inverter gets its natural balance as Meynard and Foch describes in (Meynard et al 2002) Figure 8b show a detail of voltage VC2(t) and iC2(t) current in flying capacitor named C2 working as resonant mode the ripple voltage DvC2(t) is about 375 of the total voltage

VC2(t) and DiC2(t)cong25Ap-p even though the average cu-rrent throughout C2 estimated by means Originreg is about zero Then both C1 and C2 work like an ideal vol-tage source

Simulation set-up of a six cell FB-FCMI was desig-ned based on theory of experimental section Figure 9 shows the voltage in flying capacitors VC5(t)=56VDC VC4(t)=46 VDC VC3(t)=36 VDC VC2(t)=26 VDC and VC1(t)=16 VDC considering VDC = 200V The natural ba-lance in all cases is getting about tss~0075 seconds Mo-reover Figure 10 shows an evolution of capacitor voltage υC(t) expressed as function of uS3(t) in these case the output frequency in the element R is f0asymp20 kHz in so far as the command signal frequency uS3(t) opera-tes at fsw asymp 3333 kHz therefore the statement f0 = N fsw where N is the number of cell is substantiated in this work

the Fb-FCMi Coupled to high voltage appliCation

The high voltage application consists in a proposed tree-cell FB-FCMI coupled to a high voltage transfor-mer where its primary winding inductor is part of the RLC resonant-circuit and the secondary winding is cou-

ʋR(t)

ʋC(t)

ʋ0(t)

TswT6 T3 T2

Volta

ge [V

]

Time [sec]

Volta

ge [V

]Vo

ltage

[V]

Figure 6 Waveforms of the main voltages υR(t) υC(t) and υ0(t) in the FB-FCMI

Design anD simulation of a resonant full-briDge multicell power inverter for high-voltage applications

IngenIeriacutea InvestIgacIoacuten y tecnologiacutea volumen XIX (nuacutemero 3) julio-septiembre 2018 245-254 ISSN 2594-0732 FI-UNAM250

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derably reduction of power dissipation in the MOS-FETs Figure 7b shows the simulation results on instantaneous power Pi(t) and PRMS in semiconductors the RMS value is ~7 mW

the Fb-FCMi at resonant Mode siMulation set-up

The FB-FMCI showed in Figure 1 is developed and run-ning on SIMULINKMATLABreg using the SimPowerSys-tem libraries In order to get the best performance a previous calculus of RLC resonant components either SimPowerSystem or Funtional-Block was made to achieve the best tuning of the resonant condition The parameter simulation values are f= 20 kHz C=10 nF L=6333 mH R = 1Ω and VM=66 V The simulation parameters on [C1 C1rsquo] and [C2 C2rsquo] are VDC=200 V VC1=VC1rsquo= 13333 V and VC2=VC2rsquo=6666 V also the voltage response of flying ca-pacitors are shown in Figure 8a from this it is possible to sustain the correct values in open-loop control Hence the static inverter gets its natural balance as Meynard and Foch describes in (Meynard et al 2002) Figure 8b show a detail of voltage VC2(t) and iC2(t) current in flying capacitor named C2 working as resonant mode the ripple voltage DvC2(t) is about 375 of the total voltage

VC2(t) and DiC2(t)cong25Ap-p even though the average cu-rrent throughout C2 estimated by means Originreg is about zero Then both C1 and C2 work like an ideal vol-tage source

Simulation set-up of a six cell FB-FCMI was desig-ned based on theory of experimental section Figure 9 shows the voltage in flying capacitors VC5(t)=56VDC VC4(t)=46 VDC VC3(t)=36 VDC VC2(t)=26 VDC and VC1(t)=16 VDC considering VDC = 200V The natural ba-lance in all cases is getting about tss~0075 seconds Mo-reover Figure 10 shows an evolution of capacitor voltage υC(t) expressed as function of uS3(t) in these case the output frequency in the element R is f0asymp20 kHz in so far as the command signal frequency uS3(t) opera-tes at fsw asymp 3333 kHz therefore the statement f0 = N fsw where N is the number of cell is substantiated in this work

the Fb-FCMi Coupled to high voltage appliCation

The high voltage application consists in a proposed tree-cell FB-FCMI coupled to a high voltage transfor-mer where its primary winding inductor is part of the RLC resonant-circuit and the secondary winding is cou-

ʋR(t)

ʋC(t)

ʋ0(t)

TswT6 T3 T2

Volta

ge [V

]

Time [sec]

Volta

ge [V

]Vo

ltage

[V]

Figure 6 Waveforms of the main voltages υR(t) υC(t) and υ0(t) in the FB-FCMI

251

Flores-Fuentes AllAn Antonio Peacuterez-MArtiacutenez Joseacute Arturo GArciacuteA-MeJiacuteA JuAn FernAndo rossAno-diacuteAz ivaacuten osvAldo torres-reyes cArlos eduArdo

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14980 14985 14990 14995120

125

130

135

V C2(t)

Time [ms]

VC2(t) iC2(t)

-5

0

5

10

15

i C2(t)

Figure 8 a) Flying Capacitors voltage response VC1(t) and VC2(t) b) Detail of voltage VC2(t) and current iC2(t) at resonant mode

6960 6965 6970 6975 6980

-50

-25

0

25

50

75

V M

N(t) [V

]

Time [ms]

IMN(t) VMN(t) -10

-5

0

5

10

15

I MN(t)

[A]

Figure 7 The Zero-Current Switching (ZCS) a) Voltage VMN(t) and current IMN(t) through the MOSFET b) Instantaneous Pi(t) and PRMS power behavior

16middotVDC

VDC

Volta

ge [V

]

VC5(t)

VC4(t)

VC3(t)

VC2(t)

VC1(t)

16middotVDC

16middotVDC

16middotVDC

16middotVDC

16middotVDC

Time [s]tss

VDC

Figure 9 Voltage response in flying capacitors in a six cell FB-FCMI at resonant mode

a) b)

Design anD simulation of a resonant full-briDge multicell power inverter for high-voltage applications

IngenIeriacutea InvestIgacIoacuten y tecnologiacutea volumen XIX (nuacutemero 3) julio-septiembre 2018 245-254 ISSN 2594-0732 FI-UNAM252

DOI httpdxdoiorg1022201fi25940732e201819n3021

pled an equivalent electrical model of Dielectric Barrier Discharge see Figure 1 The DBD model involves a stray capacitance CS due to effect of the capacitance reactor two dielectric capacitance Cd1 and Cd2 corresponding to dielectric material as glass then a parallel circuit is for-med first by a series load Rg-Cg and second by a cu-rrent source controlled by voltage Vg Figure 11 shows the schematic and equivalent DBD proposed in (Flores et al 2009)

The goal of proposed of an electrical model is to provide more information about voltage and current values at the electrical discharge because in the experi-mental set-up not only the voltages υd(t) and υg(t)

are not measurable but also parameters are not well known because there are not conventional methods with mea-surement instruments Therefore after simulation pro-cesses in SIMULINKMATLABreg the voltages and currents in the DBD are shown in Figure 12

Finally a simulation of DBD running in helium gas and driven by the resonant tree-cell FB-FCMI which deliver electric power through primary winding towards DBD coupled in the secondary side Thereby Figure 12 shows the electrical behavior of voltage υs(t) and current is(t) typically in a DBD taking in account literature information in (Flores et al 2009) and consi-dering parameters as

a) type of ionized gasb) applied voltage υs(t)c) current discharge is(t)d) operation frequency 20 kHze) reactor geometry

In the simulation results voltage υs(t) and current is(t) are out of phase because DBD load is predominantly capacitive as shown in the electrical model of Figure 11 This is an intrinsic characteristic of the electrical DBD behavior however the system is in resonant mode operation but the total power consumption by electri-cal discharge is in the order of units of watts and effi-ciency is ~20 (Flores et al 2009)

conclusIons

The simulation of a FB-FCMI at resonant mode is pre-sented The command control generates twelve signals at Fundamental Frequency strategy operating at fsw=f0N where N is the total number of cells in the static inverter The statement about relation between output frequency and commutation frequency is given by fo=Nfsw in this work in order to validate that condition from this kind of power static inverter not only a three-

Figure 10 Voltage υR(t) operating at f0=6fsw expressed as function of uS3(t) at fsw

Figure 11 Electrical model of the DBD

Figure 12 Simulation set-up of DBD in helium

Design anD simulation of a resonant full-briDge multicell power inverter for high-voltage applications

IngenIeriacutea InvestIgacIoacuten y tecnologiacutea volumen XIX (nuacutemero 3) julio-septiembre 2018 245-254 ISSN 2594-0732 FI-UNAM252

DOI httpdxdoiorg1022201fi25940732e201819n3021

pled an equivalent electrical model of Dielectric Barrier Discharge see Figure 1 The DBD model involves a stray capacitance CS due to effect of the capacitance reactor two dielectric capacitance Cd1 and Cd2 corresponding to dielectric material as glass then a parallel circuit is for-med first by a series load Rg-Cg and second by a cu-rrent source controlled by voltage Vg Figure 11 shows the schematic and equivalent DBD proposed in (Flores et al 2009)

The goal of proposed of an electrical model is to provide more information about voltage and current values at the electrical discharge because in the experi-mental set-up not only the voltages υd(t) and υg(t)

are not measurable but also parameters are not well known because there are not conventional methods with mea-surement instruments Therefore after simulation pro-cesses in SIMULINKMATLABreg the voltages and currents in the DBD are shown in Figure 12

Finally a simulation of DBD running in helium gas and driven by the resonant tree-cell FB-FCMI which deliver electric power through primary winding towards DBD coupled in the secondary side Thereby Figure 12 shows the electrical behavior of voltage υs(t) and current is(t) typically in a DBD taking in account literature information in (Flores et al 2009) and consi-dering parameters as

a) type of ionized gasb) applied voltage υs(t)c) current discharge is(t)d) operation frequency 20 kHze) reactor geometry

In the simulation results voltage υs(t) and current is(t) are out of phase because DBD load is predominantly capacitive as shown in the electrical model of Figure 11 This is an intrinsic characteristic of the electrical DBD behavior however the system is in resonant mode operation but the total power consumption by electri-cal discharge is in the order of units of watts and effi-ciency is ~20 (Flores et al 2009)

conclusIons

The simulation of a FB-FCMI at resonant mode is pre-sented The command control generates twelve signals at Fundamental Frequency strategy operating at fsw=f0N where N is the total number of cells in the static inverter The statement about relation between output frequency and commutation frequency is given by fo=Nfsw in this work in order to validate that condition from this kind of power static inverter not only a three-

Figure 10 Voltage υR(t) operating at f0=6fsw expressed as function of uS3(t) at fsw

Figure 11 Electrical model of the DBD

Figure 12 Simulation set-up of DBD in helium

253

Flores-Fuentes AllAn Antonio Peacuterez-MArtiacutenez Joseacute Arturo GArciacuteA-MeJiacuteA JuAn FernAndo rossAno-diacuteAz ivaacuten osvAldo torres-reyes cArlos eduArdo

IngenIeriacutea InvestIgacIoacuten y tecnologiacutea volumen XIX (nuacutemero 3) julio-septiembre 2018 245-254 ISSN 2594-0732 FI-UNAM

DOI httpdxdoiorg1022201fi25940732e201819n3021

cell flying capacitor inverter was designed but also a six-cell inverter was simulated So the natural balance of the voltage in flying capacitors at open-loop control in both cases is correct achieved The RLC passive ele-ments are designed based on the resonance frequency which is the same that the output inverter frequency f0=20 kHz hence optimal coupling between RLC and FB-FCMI was successfully set-up simulated in MAT-LABreg Because of resonant condition the semiconductor devices operate at ZCS mode properly so the dvdt snu-bber circuit protection is reduced in its size Finally a full system conformed by FB-FCMI coupled at DBD electrical model is running on SIMULINKMATLABreg in order to prove the high voltage application to generate electrical discharges in helium gas

Aknowledgements

The authors wish to thank COMECYT for financial sup-port and MRS Saacutemano-Aacutengeles Antonio director of the Centro Universitario UAEMex Atlacomulco

references

Aguilloacuten-Garciacutea J Fernaacutendez-Nava JM Bantildeuelos-Saacutenchez P Unbalanced volage effects on a single phase multilevel inver-ter due to control strategies 26th Annual International Tele-communications Energy Conference INTELEC 2004 volume 19 Chicago EU September 2004 pp 140-145

Abu-Rub H Holtz J Rodriguez J Medium-Voltage Multilevel Converters State of the Art Challenges and Requirements in Industrial Applications IEEE Transactions on Industrial Appli-cations volume 57 (issue 8) 2010 2581-2596

Fernao-Pires V Martins JF Foito D Chen H A grid connected photovoltaic system with a multilevel inverter and a Le-Blanc transformer International Journal of Renewable Energy Research volume 2 (issue 2) 2012 84-91

Flores-Fuentes AA Pentildea-Eguiluz R Loacutepez-Callejas R Merca-do-Cabrera A Valencia-Alvarado R Barocio-Delgado S De la Piedad-Beneitez A Electrical model of an atmospheric pressure dielectric barrier discharge cell IEEE Transaction on Plasma Science volume 37 (issue 1) 2009 128-134

Hirofumi A The state-of-the-art of power electronics in Japan IEEE Transactions on Power Electronics volume 13 (issue 2) 1998 345-356

Holmes D and Lipo T Pulse width modulation for power converter Principles and practice 1st ed Piscataway NY IEEE Press Wi-ley 2003 pp 600-724

Loacutepez-Fernaacutendez JA Pentildea-Eguiluz R Member IEEE Loacutepez-Ca-llejas R Mercado-Cabrera A Jaramillo-Sierra B Rodriacuteguez-Meacutendez B Valencia-Alvarado R Muntildeoz-Castro AE A 10- to 30-kHz adjustable frequency resonant full-bridge multicell power converter IEEE Transactions on Industrial Electronics volume 62 (issue 4) 2015 2215-2223

Loren L New power semiconductor components for future inno-vate high frequency power converters IEEE International Conference on Industrial Technology volume 2 Maribor Slo-venia December 2003 1173-1177

Meynard TA Foch H Thomas P Courault J Jakdo R Nahrs-taedt M Multicell Converters Basic Concepts and Industry Applications IEEE Transactions on Industrial Electronics volu-me 49 (issue 5) 2002 955-964

Peacutentildea-Eguiluz R Loacutepez-Fernaacutendez JA Mercado-Cabrera A Ja-ramillo-Sierra B Loacutepez-Callejas R Rodriacuteguez-Meacutendez B Valencia-Alvarado R Flores-Fuentes AA Muntildeoz-Castro AE Plasma Science and Technology volume 19 2017 1-10

Rodriguez J Jih-Sheng L Fang-Zheng P Multilevel inverters a survey of topologies controls and applications IEEE on In-dustrial Electronics volume 49 (issue 4) 2002 724-738

Rodriacuteguez J Kazimierkowski MP Espinoza JR State of the art of finite control set model predictive control in power electro-nics IEEE Transactions on Industrial Informatics volume 9 (is-sue 2) 2012 1003-1016

Samir K Malinowski M Gopakumar KRecent advances and in-dustrial applications of multilevel converters IEEE on Indus-trial Electronics volume 57 (issue 8) 2010 2553-2580

Tolbert LM Peng FZ Multilevel converters as a utility interface for renewable energy systems Power Engineering Society Summer Meeting 16-20 July 2000 Seattle WA USA

Zhe C Guerrero JM Blaabjerg F A Review of the state of the art of power electronics for wind turbines IEEE Transactions on Power Electronics volume 24 (issue 8) 2009 1859-1875

Design anD simulation of a resonant full-briDge multicell power inverter for high-voltage applications

IngenIeriacutea InvestIgacIoacuten y tecnologiacutea volumen XIX (nuacutemero 3) julio-septiembre 2018 245-254 ISSN 2594-0732 FI-UNAM254

DOI httpdxdoiorg1022201fi25940732e201819n3021

Suggested citation

Chicago style citation

Flores-Fuentes Allan Antonio Joseacute Arturo Peacuterez-Martiacutenez Juan Fer-nando Garciacutea-Mejiacutea Ivaacuten Osvaldo Rossano-Diacuteaz Carlos Eduardo Torres-Reyes Design and simulation of a resonant full-bridge multi-cell power inverter for high-voltage applications Ingenieriacutea Investiga-cioacuten y Tecnologiacutea XIX 03 (2018) 245-254

ISO 690 citation style

Flores-Fuentes AA Peacuterez-Martiacutenez JA Garciacutea-Mejiacutea JF Rossano-Diacuteaz IO Torres-Reyes CE Design and simulation of a resonant full-bridge multicell power inverter for high-voltage applications Ingenieriacutea Investigacioacuten y Tecnologiacutea volumen XIX (issue 3) July-Sep-tember 2018 245-254

About the Authors

Flores-Fuentes Allan Antonio Ph D degree in electronics engineering by Instituto Tec-noloacutegico de Toluca Meacutexico 2009 Since 2011 he has been working in the Univer-sidad Autoacutenoma del Estado de Meacutexico His research interest includes multilevel static converters applied to industrial applications pulsed power supplies and instrumentation and control systems

Peacuterez-Martiacutenez Joseacute Arturo PhD degree in Electronic engineering from the Instituto Tecnoloacutegico de Toluca Toluca Mexico since 2010 His research concerns in static RF converter applied to plasma micro-discharges in different configuration reac-tors and control systems also the automation of advanced manufacturing proces-ses He is working in the Universidad Autoacutenoma del Estado de Meacutexico Centro Universitario UAEM Atlacomulco Meacutexico

Garciacutea-Mejiacutea Juan Fernando Received the title of Engineer in Electronics from the Ins-tituto Tecnoloacutegico de Toluca in 2004 he obtained the degree of Master of Science in Electronics by the same institution Since 2004 he has been working at the Cen-tro Universitario UAEM Atlacomulco where he is a full-time professor with PRODEP profile and leader of the academic group ldquoSoftware Development De-vices and Systems Applied to the Technological Innovationrdquo his research line is focused on the development of virtual instruments and the use of softcomputing techniques applied to control engineering

Rossano-Diacuteaz Ivaacuten Osvaldo MA Engineer in electronics by Instituto Tecnoloacutegico de Toluca Meacutexico 2004 Since 2009 he has been with the Universidad Autoacutenoma del Estado de Meacutexico where he is currently a Reacher His research interest include Sliding control Digital control static converters and control applied to Bioelec-tronics Systems

Torres-Reyes Carlos Eduardo BSc degree in electronic engineering from the Instituto Tecnoloacutegico de Toluca Toluca Mexico in 2002 also he received the PhD degree in the same institution in 2010 Actually he works in the CU Atlacomulco of the Universidad Autoacutenoma del Estado de Meacutexico in developing of plasma torch power supply and associated electronic devices